I. To assess the relative activity of trametinib (mitogen-activated protein kinase [MEK] inhibitor) alone or in combination with GSK2141795 (AKT inhibitor) for patients with recurrent or persistent endometrial cancer by progression-free survival. (Phase II) II. To determine the frequency and severity of adverse events as assessed by Common Terminology Criteria for Adverse Events (CTCAE). (Phase II) III. To determine the tolerability of the combination regimen of trametinib and GSK2141795 through determination of dose-limiting toxicity in a two-stage safety lead in study. (Safety assessment lead-in)